Periodic Loop Solutions and Their Limit Forms for the Kudryashov-Sinelshchikov Equation

نویسندگان

  • Bin He
  • Qing Meng
  • Jinhua Zhang
  • Yao Long
  • Stefano Lenci
چکیده

A mixture of liquid and gas bubbles of the same size may be considered as an example of a classic nonlinear medium. In practice, analysis of propagation of the pressure waves in a liquid with gas bubbles is important problem. We know that there are solitary and periodic waves in a mixture of a liquid and gas bubbles and these waves can be described by nonlinear partial differential equations. As for examples of nonlinear differential equations to describe the pressure waves in bubbly liquids, we can point out the Burgers equation, the Korteweg-de Vries equation, the Burgers-Korteweg-de Vries equation, and so on 1 . In 2010, Kudryashov and Sinelshchikov 1 obtained amore common nonlinear partial differential equation for describing the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer, and the equation reads as follows:

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exact Solutions of the Kudryashov-Sinelshchikov Equation by Modified exp-Function Method

In this paper, the modified exp-function method is used to seek generalized wave solutions of Kudryashov-Sinelshchikov equation. As a result, some new types of exact traveling wave solutions for arbitrary α, β are obtained which include exponential function, hyperbolic function and trigonometric function. The related results are extend. Obtained results clearly indicate the reliability and effi...

متن کامل

F-Expansion Method and Its Application for Finding New Exact Solutions to the Kudryashov-Sinelshchikov Equation

Based on the F-expansion method, and the extended version of F-expansion method, we investigate the exact solutions of the Kudryashov-Sinelshchikov equation.With the aid ofMaple, more exact solutions expressed by Jacobi elliptic function are obtained. When themodulusmof Jacobi elliptic function is driven to the limits 1 and 0, some exact solutions expressed by hyperbolic function solutions and ...

متن کامل

Exact solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation via the first integral method

Nonlinear evolution equations are widely used to describe complex phenomena in various sciences such as fluid physics, condensed matter, biophysics, plasma physics, nonlinear optics, quantum field theory and particle physics, etc. In recent years, various powerful methods have been presented for finding exact solutions of the nonlinear evolution equations in mathematical physics, such as, tanh ...

متن کامل

Exact solutions of equations for the Burgers hierarchy

Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented. The solutions for this hierarchy are obtained by using the generalized Cole Hopf transformation.

متن کامل

A note on ” New abundant solutions for the Burgers equation ”

Salas, Gomez and Heranańdez [A.Y. Salas S., C.A. Gomez S., J.E.C Hernańdez, New abundant solutions for tha Burgers equation, Computers and Mathematics with Applications 58 (2009) 514 -520] presented 70 ”new exact solutions” of a ”generalized version” of the Burgers equation. In this comment we show that all 70 solutions by these authors are not new and cannot be new. PACS: 02.30.Jr Ordinary dif...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014